Question

Shoppers enter Hamilton Place Mall at an average of 10 per five minute intervals (or 120 per hour)

a. What is the probability that exactly 5 shoppers enter the mall between noon and
12:05 p.m.?

b. What is the probability that at least 2(i.e. 2 or more) shoppers enter the mall between 5:00 and 5:05 p.m.?

c. If the number of shoppers entering the mall in different hours are independent of one another, find the expected number of shoppers entering the mall between 9:00 am and 9:00 p.m.

Answer 1

a)

between noon and 12:05 pm, time = 5 min

hence mean = 10

X follow poisson distribution

P(X = 5) = e^(-10) * 10^5/5!

= 0.0378

b)

again X follow poisson with mean = 10

P(X >= 2) = 1- P(X =0) - P(X = 1)

= 1- e^(-10)(1+10)

= 0.9995

c)

there are 12 hours b/w 9 am and 9 pm

hence

12 * 120

= 1440

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